Modus Tollens (MT) is a classical inference rule, counterfactuals are hypothetical statements that contradict facts, and counterfactual reasoning is the process of reasoning based on such statements. Negation is a core notion in all three. This paper adopts the logical systems LCOI and PLCOI and introduces three kinds of negation—contradictory, opposite, and intermediary—to construct three variants of Modus Tollens, denoted MTC, MTO, and MTI respectively. For each system we formalize implication and present a truth‑value algorithm; for example, in MTC, if premise $P$ is true then the truth value of conclusion $Q$ equals the truth value of the second premise $\neg_{c} P$, where $\neg_{c}$ denotes contradictory negation. We discuss the reducibility of these algorithms. To embed the three negations into counterfactuals and their reasoning, we split counterfactuals into two categories based on the presence of logical negation and propose three counterfactual forms based on contradictory, opposite, and intermediary negation. We prove that the inference structures of these three counterfactual reasonings correspond exactly to MTC, MTO, and MTI, sharing the same logical pattern. Consequently, the truth‑value algorithms for MTC, MTO, and MTI serve as the algorithms for the respective counterfactual reasonings. The algorithms indicate that when the first premise of a reasoning is true, the truth value of the conclusion matches the truth value of the corresponding negative premise, demonstrating consistency and accuracy.
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